Question Number 154343 by Lekhraj last updated on 17/Sep/21 Answered by qaz last updated on 17/Sep/21 $$\frac{\mathrm{sin}\:\mathrm{x}}{\bullet\mathrm{O}}=\frac{\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C}}{\mathrm{OC}},\:\:\:\:\:\:\frac{\mathrm{sin}\:\mathrm{30}°}{\bullet\mathrm{O}}=\frac{\mathrm{sin}\:\mathrm{105}°}{\mathrm{OA}} \\ $$$$\because\:\:\mathrm{OA}=\mathrm{OC}\:\:\:\:\:\: \\ $$$$\therefore\:\:\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{sin}\:\mathrm{30}°}{\mathrm{sin}\:\mathrm{105}°}\centerdot\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\mathrm{sin}\:\angle\mathrm{M}\bullet\mathrm{C} \\ $$$$\because\:\:\:\angle\mathrm{M}\bullet\mathrm{C}=\mathrm{180}°−\mathrm{135}°−\mathrm{x}=\mathrm{45}°−\mathrm{x} \\ $$$$\therefore\:\:\:\mathrm{sin}\:\mathrm{x}=\frac{\sqrt{\mathrm{2}}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}+\mathrm{1}}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)…
Question Number 23262 by ajfour last updated on 28/Oct/17 Commented by ajfour last updated on 28/Oct/17 $$\frac{{CN}}{{AC}}=\frac{{x}}{{x}+{y}}\:\:\:;\:\:\:\frac{{AN}}{{AC}}=\frac{{y}}{{x}+{y}} \\ $$$$\frac{{MB}}{{AB}}\:=\frac{{y}}{{x}+{y}}\:;\:\:\frac{{AM}}{{AB}}=\frac{{x}}{{x}+{y}}\:. \\ $$$${based}\:{on}\:{similarity}\:\:{of}\:{triangles}. \\ $$$$\bigtriangleup{CNP}\:\sim\:\bigtriangleup{CAB} \\ $$$$\Rightarrow\:\:\frac{{CN}}{{AC}}=\frac{{NP}\left(={AM}\right)}{{AB}}=\frac{{CP}}{{BC}}…
Question Number 23253 by ajfour last updated on 28/Oct/17 Commented by ajfour last updated on 28/Oct/17 $${Q}.\mathrm{23251}\:\left({solution}\right) \\ $$ Commented by math solver last updated…
Question Number 23251 by math solver last updated on 28/Oct/17 Commented by math solver last updated on 28/Oct/17 $$\mathrm{q}.\mathrm{19}\:? \\ $$ Terms of Service Privacy…
Question Number 154306 by amin96 last updated on 16/Sep/21 Commented by som(math1967) last updated on 17/Sep/21 $${see}\:{Qno}\:\mathrm{152486} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 23226 by ajfour last updated on 27/Oct/17 Commented by ajfour last updated on 27/Oct/17 $${Q}.\mathrm{23212}\:\:\left({solution}\right) \\ $$ Commented by math solver last updated…
Question Number 88758 by mr W last updated on 12/Apr/20 $${Some}\:{people}\:{may}\:{have}\:{noticed}\:{that}\:{i} \\ $$$${usually}\:{calculate}\:{areas}\:{concerning} \\ $$$${parabola}\:{directly},\:{without}\:{applying} \\ $$$${complicated}\:{integral}\:{calculus}. \\ $$$${Here}\:{i}\:{am}\:{giving}\:{you}\:{the}\:{backgroud}.\: \\ $$$${Actually}\:{you}\:{know}\:{all}\:{these}\:{things}\:{and} \\ $$$${you}\:{are}\:{able}\:{to}\:{prove}\:{them}.\:{Maybe} \\ $$$${you}\:{just}\:{forget}\:{to}\:{apply}\:{them}.…
Question Number 88754 by ajfour last updated on 12/Apr/20 Commented by mr W last updated on 13/Apr/20 $${there}\:{is}\:{no}\:{unique}\:{solution}\:{for}\:\frac{{b}}{{a}}. \\ $$$${we}\:{can}\:{only}\:{find}\:{the}\:{correlation}\:{between} \\ $$$${a}\:{and}\:{b}. \\ $$ Commented…
Question Number 23212 by math solver last updated on 27/Oct/17 Commented by math solver last updated on 27/Oct/17 $$\mathrm{q}.\mathrm{13}\:\mathrm{plz}\:? \\ $$ Answered by ajfour last…
Question Number 88731 by I want to learn more last updated on 12/Apr/20 Commented by john santu last updated on 12/Apr/20 $$\left.\mathrm{2}\left.{a}\right)\:\frac{{dy}}{{dx}}\:=\:{kx}−\mathrm{48}{x}^{−\mathrm{3}} \:\right]_{\left(−\mathrm{2},\mathrm{14}\right)} \:=\:\mathrm{0} \\…